Question: Rewrite as a simplified fraction. ${3.56\overline{1} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3561.1111...\\ 100x &= 356.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3205}$ ${x = \dfrac{3205}{900}} $ ${x = \dfrac{641}{180}} \text{or} {3 \dfrac{101}{180}}$